Filtering and Deconvolution

Abstract

Estimating a remote signal from the measurements of another observed signal is a classical problem of today. Among the possible facets the problem can take, we will assume herein that the two signals are related each other by a dynamical system in state–space form. To be precise assume that the observed signal y(·) and the remote signal z(·) obey the following equations:

x(t +1) = A(t)x(t)+B(t)w(t)

y(t) = C(t)x(t)+D(t)w(t)

z(t) = E(t)x(t)+N(t)w(t),

where w(·) is a disturbance.